SOLUTION: Solve. t2 + 4t = 1

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Question 552892: Solve.
t2 + 4t = 1


Answer by jim_thompson5910(35256) About Me  (Show Source):
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t%5E2%2B4t=1 Start with the given equation.


t%5E2%2B4t-1=0 Get every term to the left side.


Notice that the quadratic t%5E2%2B4t-1 is in the form of At%5E2%2BBt%2BC where A=1, B=4, and C=-1


Let's use the quadratic formula to solve for "t":


t+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


t+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%281%29%28-1%29+%29%29%2F%282%281%29%29 Plug in A=1, B=4, and C=-1


t+=+%28-4+%2B-+sqrt%28+16-4%281%29%28-1%29+%29%29%2F%282%281%29%29 Square 4 to get 16.


t+=+%28-4+%2B-+sqrt%28+16--4+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-1%29 to get -4


t+=+%28-4+%2B-+sqrt%28+16%2B4+%29%29%2F%282%281%29%29 Rewrite sqrt%2816--4%29 as sqrt%2816%2B4%29


t+=+%28-4+%2B-+sqrt%28+20+%29%29%2F%282%281%29%29 Add 16 to 4 to get 20


t+=+%28-4+%2B-+sqrt%28+20+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


t+=+%28-4+%2B-+2%2Asqrt%285%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


t+=+%28-4%29%2F%282%29+%2B-+%282%2Asqrt%285%29%29%2F%282%29 Break up the fraction.


t+=+-2+%2B-+sqrt%285%29 Reduce.


t+=+-2%2Bsqrt%285%29 or t+=+-2-sqrt%285%29 Break up the expression.


So the solutions are t+=+-2%2Bsqrt%285%29 or t+=+-2-sqrt%285%29


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Jim